Strength Pareto Evolutionary Algorithm is a Multiple Objective Optimization (MOO) algorithm and an Evolutionary Algorithm from the field of Evolutionary Computation. It belongs to the field of Evolutionary Multiple Objective (EMO) algorithms. Refer to for more information and references on Multiple Objective Optimization.
Strength Pareto Evolutionary Algorithm is an extension of the Genetic Algorithm for multiple objective optimization problems.
It is related to sibling Evolutionary Algorithms such as Non-dominated Sorting Genetic Algorithm (NSGA), Vector-Evaluated Genetic Algorithm (VEGA), and Pareto Archived Evolution Strategy (PAES).
There are two versions of SPEA, the original SPEA algorithm and the extension SPEA2. Additional extensions include SPEA+ and iSPEA.

The objective of the algorithm is to locate and and maintain a front of non-dominated solutions, ideally a set of Pareto optimal solutions.
This is achieved by using an evolutionary process (with surrogate procedures for genetic recombination and mutation) to explore the search space, and a selection process that uses a combination of the degree to which a candidate solution is dominated (strength) and an estimation of density of the Pareto front as an assigned fitness. An archive of the non-dominated set is maintained separate from the population of candidate solutions used in the evolutionary process, providing a form of elitism.

Algorithm (below) provides a pseudocode listing of the Strength Pareto Evolutionary Algorithm 2 (SPEA2) for minimizing a cost function.
The CalculateRawFitness function calculates the raw fitness as the sum of the strength values of the solutions that dominate a given candidate, where strength is the number of solutions that a give solution dominate.
The CandidateDensity function estimates the density of an area of the Pareto front as $\frac{1.0}{\sigma^k + 2}$ where $\sigma^k$ is the Euclidean distance of the objective values between a given solution the $k$th nearest neighbor of the solution, and $k$ is the square root of the size of the population and archive combined.
The PopulateWithRemainingBest function iteratively fills the archive with the remaining candidate solutions in order of fitness.
The RemoveMostSimilar function truncates the archive population removing those members with the smallest $\sigma^k$ values as calculated against the archive.
The SelectParents function selects parents from a population using a Genetic Algorithm selection method such as binary tournament selection. The CrossoverAndMutation function performs the crossover and mutation genetic operators from the Genetic Algorithm.

Listing (below) provides an example of the Strength Pareto Evolutionary Algorithm 2 (SPEA2) implemented in the Ruby Programming Language.
The demonstration problem is an instance of continuous multiple objective function optimization called SCH (problem one in [Deb2002]). The problem seeks the minimum of two functions: $f1=\sum_{i=1}^n x_{i}^2$ and $f2=\sum_{i=1}^n (x_{i}-2)^2$, $-10\leq x_i \leq 10$ and $n=1$. The optimal solutions for this function are $x \in [0,2]$.
The algorithm is an implementation of SPEA2 based on the presentation by Zitzler, Laumanns, and Thiele [Zitzler2002].
The algorithm uses a binary string representation (16 bits per objective function parameter) that is decoded and rescaled to the function domain. The implementation uses a uniform crossover operator and point mutations with a fixed mutation rate of $\frac{1}{L}$, where $L$ is the number of bits in a solution's binary string.

Zitzler and Thiele introduced the Strength Pareto Evolutionary Algorithm as a technical report on a multiple objective optimization algorithm with elitism and clustering along the Pareto front [Zitzler1998]. The technical report was later published [Zitzler1999].
The Strength Pareto Evolutionary Algorithm was developed as a part of Zitzler's PhD thesis [Zitzler1999a].
Zitzler, Laumanns, and Thiele later extended SPEA to address some inefficiencies of the approach, the algorithm was called SPEA2 and was released as a technical report [Zitzler2001] and later published [Zitzler2002]. SPEA2 provides fine-grained fitness assignment, density estimation of the Pareto front, and an archive truncation operator.

Zitzler, Laumanns, and Bleuler provide a tutorial on SPEA2 as a book chapter that considers the basics of multiple objective optimization, and the differences from SPEA and the other related Multiple Objective Evolutionary Algorithms [Zitzler2004].